I had somewhat success using oxy rug spot cleaner as a last resort.
He was washing them the other day and, just giving up really, as a last resort got the Lava bar soap and rubbed it on the soil.
This is only as a last resort on something that might be tossed otherwise. These shirts were the non-wrinkle type with 60% cotton and 40%.
By the way, these shirts (while very inexpensive) are absolutely the best for wrinkle-free that I've come across.
They are the Stafford brand. I bought them at J.C. Penney about 3 years ago---bought 3 and he wears them every day in the spring, summer, and early fall. (This is Texas weather.)
Just thought this might help some poor soul with ring-around-the-collar.
P.S. I have heard that at the Brooks Brothers outlets they sell a wonderful wrinkle-free dress shirt. I was told by a colleague who wears a suit every day and who travels a lot--ergo the need for wrinkle-free.